Portable music players are often directly compatible with your new Linux computer as a plug-and-play device. Plug the player into your computer's USB port with whatever cable it came with, and the player will mount as if it were an external harddrive. Drag your music to the appropriate folder, your audiobooks to their folder, photos to their folder, and so on.
A notable exception to this is the Apple iPod and other iDevices, which generally require iTunes, which only runs on Mac or Windows. See the previous section for details.
Some media players have two settings: to be seen as a media player that requires an iTunes-like interface, or as a USB harddrive that has no requirements. If you try to mount your media player on your new Linux computer and nothing happens, try disconnecting and looking in the Settings or System menus of your media player and changing its mode.
If you're looking for a media player, try to purchase one that follows open standards and plays nice with all computing platforms. Some popular iPod-alternatives are the Sansa line of media players (you might know them also as SanDisk, manufacturer of popular USB thumbdrives), the Cowon Jet Audio series, and the Archos Android series.